Metamath Proof Explorer

Theorem s1nz

Description: A singleton word is not the empty string. (Contributed by Mario Carneiro, 27-Feb-2016) (Proof shortened by Kyle Wyonch, 18-Jul-2021)

Ref Expression
Assertion s1nz 
|- <" A "> =/= (/)

Proof

Step Hyp Ref Expression
1 df-s1 
 |-  <" A "> = { <. 0 , ( _I ` A ) >. }
2 opex 
 |-  <. 0 , ( _I ` A ) >. e. _V
3 2 snnz 
 |-  { <. 0 , ( _I ` A ) >. } =/= (/)
4 1 3 eqnetri 
 |-  <" A "> =/= (/)